Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
日本語の概要は準備中です。原文の説明を表示しています。
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概要と使いどころ
Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level biomechanics covering musculoskeletal mechanics, gait analysis, joint biomechanics, soft tissue mechanics, bone mechanics, and sports biomechanics.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level oceanography covering physical, chemical, biological, and geological oceanography, ocean circulation, thermohaline circulation, tides, and ocean-climate interactions.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level numerical methods knowledge. Use when working with root finding, numerical integration, numerical differentiation, interpolation, numerical linear algebra, ODEs, PDEs, or optimization algorithms. Also use when the user mentions 'Newton method', 'bisection', 'Runge-Kutta', 'finite difference', 'finite element', 'interpolation', 'numerical integration', 'quadrature', 'iterative solvers', 'condition number', 'round-off error', or 'truncation error'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level real analysis knowledge. Use when working with limits, continuity, differentiability, Riemann and Lebesgue integration, sequences and series of functions, metric spaces, measure theory, or functional analysis foundations. Also use when the user mentions 'epsilon-delta', 'uniform continuity', 'uniform convergence', 'Lebesgue integral', 'measure theory', 'sigma-algebra', 'Banach space', 'Hilbert space', 'completeness', 'compactness', 'Heine-Borel', or 'dominated convergence'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level evolutionary biology covering natural selection, genetic drift, molecular evolution, phylogenetics, speciation, macroevolution, and the modern synthesis.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level electrochemistry knowledge. Use when working with electrochemical cells, electrode potentials, Nernst equation, electrolysis, batteries, fuel cells, corrosion, electroplating, or electroanalytical methods. Also use when the user mentions 'galvanic cell', 'electrolytic cell', 'electrode potential', 'Nernst equation', 'overpotential', 'Butler-Volmer', 'battery', 'fuel cell', 'corrosion', 'electroplating', 'cyclic voltammetry', or 'impedance spectroscopy'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level ecology covering population ecology, community ecology, ecosystem ecology, food webs, energy flow, nutrient cycling, biodiversity, and conservation biology.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level differential equations knowledge. Use when working with ordinary differential equations, partial differential equations, systems of ODEs, Laplace transforms, Fourier methods, boundary value problems, stability analysis, or numerical methods for ODEs. Also use when the user mentions 'ODE', 'PDE', 'initial value problem', 'boundary value problem', 'Laplace transform', 'separation of variables', 'eigenvalue problem', 'heat equation', 'wave equation', 'Laplace equation', 'stability', or 'phase plane'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level biochemistry knowledge. Use when working with proteins, enzymes, metabolism, DNA, RNA, carbohydrates, lipids, cell signaling, or bioenergetics. Also use when the user mentions 'enzyme kinetics', 'metabolism', 'glycolysis', 'Krebs cycle', 'DNA replication', 'protein folding', 'amino acids', 'ATP', 'oxidative phosphorylation', 'gene expression', 'lipid bilayer', or 'signal transduction'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level biochemistry from a biology perspective covering metabolic pathways, enzyme kinetics, bioenergetics, signal transduction, and the biochemical basis of cellular processes.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level special relativity knowledge. Use when working with Lorentz transformations, time dilation, length contraction, relativistic energy, mass-energy equivalence, spacetime, four-vectors, or relativistic mechanics. Also use when the user mentions 'Lorentz transformation', 'time dilation', 'length contraction', 'E=mc2', 'spacetime', 'four-vector', 'relativistic momentum', 'light cone', 'proper time', 'Minkowski', or 'relativistic velocity addition'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level analytical chemistry knowledge. Use when working with chromatography, spectroscopy, electroanalytical methods, sample preparation, quantitative analysis, calibration, statistics, or instrumental analysis. Also use when the user mentions 'HPLC', 'GC', 'mass spectrometry', 'atomic absorption', 'ICP', 'titration', 'calibration curve', 'detection limit', 'NMR', 'chromatography', 'electrochemistry', 'sample preparation', or 'method validation'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level thermodynamics knowledge. Use when working with heat, temperature, entropy, thermodynamic laws, heat engines, refrigerators, phase transitions, statistical mechanics, or thermodynamic cycles. Also use when the user mentions 'entropy', 'enthalpy', 'Carnot', 'heat engine', 'thermodynamic cycle', 'ideal gas', 'phase transition', 'Gibbs free energy', 'specific heat', 'thermal equilibrium', or 'second law'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level statistics knowledge. Use when working with probability distributions, hypothesis testing, regression, Bayesian statistics, statistical inference, experimental design, ANOVA, or statistical modeling. Also use when the user mentions 'p-value', 'confidence interval', 'hypothesis test', 'regression', 'ANOVA', 'chi-square', 't-test', 'Bayesian', 'maximum likelihood', 'statistical significance', 'correlation', 'normal distribution', or 'sampling distribution'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level quantum mechanics knowledge. Use when working with wave functions, Schrodinger equation, quantum states, operators, uncertainty principle, quantum tunneling, spin, angular momentum, perturbation theory, or quantum entanglement. Also use when the user mentions 'wave function', 'Schrodinger', 'Heisenberg', 'quantum state', 'eigenvalue', 'superposition', 'tunneling', 'spin', 'Hilbert space', 'Dirac notation', 'commutator', or 'quantum measurement'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level bioinformatics covering sequence analysis, structural bioinformatics, database searching, phylogenetic analysis, NGS data processing, single-cell analysis, and machine learning in biology.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level topology knowledge. Use when working with topological spaces, continuity, compactness, connectedness, metric spaces, homeomorphisms, fundamental groups, homology, manifolds, or algebraic topology. Also use when the user mentions 'open set', 'closed set', 'compactness', 'connectedness', 'homeomorphism', 'homotopy', 'fundamental group', 'covering space', 'manifold', 'homology', 'Euler characteristic', or 'topological invariant'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level number theory knowledge. Use when working with divisibility, prime numbers, modular arithmetic, congruences, Diophantine equations, cryptography, quadratic residues, or analytic number theory. Also use when the user mentions 'prime', 'divisibility', 'modular arithmetic', 'congruence', 'GCD', 'Euler totient', 'Fermat little theorem', 'Chinese remainder theorem', 'quadratic residue', 'Diophantine equation', 'RSA', or 'prime factorization'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level calculus knowledge. Use when working with limits, derivatives, integrals, multivariable calculus, vector calculus, differential equations, series, or optimization. Also use when the user mentions 'derivative', 'integral', 'limit', 'chain rule', 'gradient', 'divergence', 'curl', 'Taylor series', 'Fourier series', 'partial derivative', 'double integral', 'line integral', 'Stokes theorem', or 'Lagrange multipliers'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level complex analysis knowledge. Use when working with complex functions, holomorphic functions, Cauchy's theorem, contour integration, Laurent series, residues, conformal mappings, or analytic continuation. Also use when the user mentions 'holomorphic', 'analytic', 'Cauchy theorem', 'residue', 'contour integral', 'Laurent series', 'conformal map', 'Riemann mapping', 'Mobius transformation', 'harmonic function', 'entire function', or 'meromorphic'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level developmental biology covering embryogenesis, cell fate determination, morphogen gradients, organogenesis, stem cells, and regenerative medicine.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level condensed matter physics knowledge. Use when working with crystal structure, band theory, semiconductors, superconductivity, magnetism, phase transitions, Fermi liquids, topological materials, or strongly correlated systems. Also use when the user mentions 'band gap', 'Fermi energy', 'semiconductor', 'superconductor', 'phonon', 'crystal lattice', 'Brillouin zone', 'Bloch theorem', 'Hall effect', 'magnetism', 'phase transition', or 'topological insulator'.
日本語の概要は準備中です。原文の説明を表示しています。
Expert-level particle physics knowledge. Use when working with the Standard Model, quarks, leptons, bosons, fundamental forces, Feynman diagrams, quantum field theory, particle accelerators, or particle detectors. Also use when the user mentions 'Standard Model', 'quark', 'lepton', 'boson', 'Higgs', 'gluon', 'neutrino', 'antimatter', 'Feynman diagram', 'QCD', 'QED', 'electroweak', 'LHC', or 'particle accelerator'.
日本語の概要は準備中です。原文の説明を表示しています。